Modeling the Interplay of Ghrelin, Leptin, and Exercise on Energy Balance: A Systems Dynamics Approach

Abstract

We detail a possible mathematical model describing the dynamics of key energy substrates, regulatory hormones, appetite, and fat mass incorporating the effect of exercise. The model describes physiological responses to three mixed meals (breakfast, lunch, dinner), represented by difference-ofexponential influx functions. The size of these meal pulses is modulated by appetite, which is dynamically regulated by ghrelin and leptin concentrations. The system is formulated as set of coupled nonlinear algebraic and ordinary differential equations (ODEs), including state variables for appetite, gut glucose and lipid contents, glycemia, lipidemia, insulinemia, plasma ghrelin and leptin concentrations, weight and fat mass, as well as the effect of exercise.